Abstract. A model of coevolutioinary genetic algorithms (COGA) consisting of two populations coevolving on two-bit landscapes is investigated in terms of the eﬀects of random partnering strategy, diﬀerent population updating schemes, and changes in mutation rate and evolution rate. The analytical and numerical approaches showed that even in such a simple model, the dynamics can change dramatically with diﬀerent evolutionary scenarios in such an extent that deserves our attention from the point of view of algorithm design.